30 cubic meters of argon gas are kept under constant pressure. The gas is heated from 10.0 degrees Celsius to 293 degrees Celsius. What is the new volume of the gas?

To find the new volume of the gas, we can use the ideal gas law, which states:

PV = nRT

Where:
P is the pressure (constant)
V is the volume
n is the number of moles of the gas
R is the ideal gas constant (8.314 J/(mol K))
T is the temperature in Kelvin

First, let's convert the initial and final temperatures from Celsius to Kelvin. The Kelvin temperature scale is an absolute temperature scale with 0 K being absolute zero. To convert from Celsius to Kelvin, we add 273.15 to the Celsius value.

Initial temperature (T1) = 10.0°C + 273.15 = 283.15 K
Final temperature (T2) = 293°C + 273.15 = 566.15 K

Since the pressure (P) is constant, we can simplify the ideal gas law equation to:

V1 / T1 = V2 / T2

Where V1 and V2 are the initial and final volumes respectively.

Substituting the given values into the equation, we have:

30 m³ / 283.15 K = V2 / 566.15 K

To solve for V2, cross multiply and divide:

30 m³ * 566.15 K = V2 * 283.15 K

V2 = (30 m³ * 566.15 K) / 283.15 K

Calculating,
V2 ≈ 60.04 m³

Therefore, the new volume of the gas is approximately 60.04 cubic meters.